Statistics and GIS in environmental geochemistry — some problems and solutions

Abstract

Statistics and geographical information system (GIS) are receiving more and more attention in environmental geochemistry. However, it is important to know the functions and limitations, the advantages and disadvantages of these techniques for better understanding of their applications. Univariate statistics is useful for mean calculation, identification of probability distribution and outlier detection. Multivariate analysis plays an important role in the study of relationships among variables. However, while dealing with regionalized variables in environmental geochemistry, the conventional statistics show their shortcomings as they are based on some kind of assumptions for random variables. Spatial analysis makes use of the spatial coordinate information of the variables, and also takes the spatial correlation into consideration. However, these pure mathematical methods are still unsatisfactory as the nature of environmental geochemistry is far from being so simple. GIS provides visualization and some spatial analysis functions with much spatial information involved. An expert system is useful for classification and prediction based on various types of information. However, the rule base for expert systems in environmental geochemistry is too small, and needs to be developed. Problems and possible solutions with the application of statistics and GIS in environmental geochemistry are discussed. Examples are based on the authors' experiences in the Yangtze River basin, China, and in southeastern Sweden. Several ideas are discussed in this paper. A `robust-symmetric mean' proposed by the authors is one of the best methods for mean calculation. For the probability distribution of trace elements, the widely accepted `log-normal distribution' is only a special case of `positively skewed distributions' which is more adequate. The combination of univariate methods and PCA is used to detect outlying samples. Partial least square (PLS) regression, principal component analysis (PCA), cluster analysis, discriminant analysis and expert systems may be used to differentiate anthropogenic anomalies from the natural background. Spatial correlations among environmental geochemical variables are revealed by cross-variograms. An environmental information system, with the integration of statistics, GIS, expert systems and environmental models should be established to further the study in environmental geochemistry, as well as to provide decision support.